Polarizable continuum model interfaces

L. Frediani, R. Cammi, S. Corni, J. Tomasi, A polarizable continuum model for molecules at diffuse interfaces, J. Chem. Phys. 120, 3893 (2004)... 

One suggestion is then to assume that p vanishes except that we have a charge density on the cavity/continuum interface that is determined so that it satisfies the Poisson equation with boundary conditions. This is the strategy behind the polarizable continuum model that goes back to the beginning of the 1980s.Then s is given the value that is typical for the macroscopic solvent. 

Other Work on Water-Related Systems. Sonoda et al.61 have simulated a time-resolved optical Kerr effect experiment. In this model, which uses molecular dynamics to represent the behaviour of the extended medium, the principle intermolecular effects are generated by the dipole-induced-dipole (DID) mechanism, but the effect of the second order molecular response is also include through terms involving the static molecular / tensor, calculated by an MP2 method. Weber et al.6S have applied ab initio linear scaling response theory to water clusters. Skaf and Vechi69 have used MP2/6-311 ++ G(d,p) calculation of the a and y tensors of water and dimethylsulfoxide (DMSO) to carry out a molecular dynamics simulation of DMSO/Water mixtures. Frediani et al.70 have used a new development of the polarizable continuum model to study the polarizability of halides at the water/air interface. 

For solvation of small molecules, the polarizable continuum model (PCM) and its variants have been widely used for calculation of solvation energy. The conductor-like PCM (CPCM) model gives a concise formulation of solvent effect, in which the solvent s response to the solute polarization is represented by the presence of induced surface charges distributed on the solute-solvent interface. In this formulation, no volume polarization (extension of solute s electron distribution into the solvent region) is allowed. The induced surface charge counterbalances the electrostatic potential on the interface generated by the solute molecule. 

The QM/MM method, and the polarizable continuum method as well, are usually considered as prototypical examples of the so-called multi-scale approaches. They combine two different description levels for the chemical system in both cases, a quantum part interacts with a classical part. Indeed, the QM/MM method can easily be extended to multi-scale schemes that include more than two description levels. Examples of three level schemes are the QM/MM/Continuum [47] and QM/QM7 MM approaches [48, 49]. In the later case, the system is divided into two QM parts, which may be described with the same or different methods, and a classical MM part. Dielectric continuum models for liquid interfaces are already available [43,50, 51] and a QM/MM/Continuum partition could be imagined in this case too, for instance to describe a solute-solvent cluster interacting with a polarizable dielectric medium. Here, however, we will focus on the QM/QM /MM partition. There is not a general scheme for this kind of approach and different algorithms can be employed to describe the interaction between subsystems. The main issue is the calculation of the interaction between two quantum subsystems that are described at QM (possibly different) theoretical levels. 

The simplest interpretation of the compact-layer capacitance is represented by the Helmholtz model of the slab filled with a dielectric continuum and located between a perfect conductor (metal surface) and the outer Helmholtz plane considered as the distance of the closest approach of surface-inactive ions. Experimental determination of its thickness, zh, may be based on Eq. (12). Moreover, its dielectric permittivity, h, is often considered as a constant across the whole compact layer. Then its value can be estimated from the values of the compact-layer capacitance, for example, it gives about 6 or 10 (depending on the choice of zh) for mercury-water interface, that is, a value that is much lower than the one in the bulk water, 80. This diminution was interpreted as a consequence of the dielectric saturation of the solvent in contact with the metal surface, its modified molecular structure or the effects of spatial inhomogeneity. The effective dielectric permittivity of the compact layer shows a complicated dependence on the electrode charge, which cannot be explained by the simple hypothesis of the saturation effects on one hand or by the unperturbed bulk-solvent nonlocal polarizability on the other hand. 

The profile of an ideally smooth interface is sketched in Fig. 13.Thehalf-spacez < 0 is occupied by the ionic skeleton of the metal. This can be described, roughly, in a jellium model, as a continuum of positive charge n+ and the effective dielectric constant due to the polarizability of the bound electrons (this quantity is, with rare exceptions (Hg Sh = 2, Ag 5 = 3.5), typically close to 1 [125]). The gap 0 < z < a accounts for a nonzero distance of the closest approach of solvent molecules to the skeleton. The region of a < z < a + d stands for the first layer of solvent molecules, while z > a + d is the diffuse-layer region. n(z) denotes the profile of the density of free electrons. This is, of course, an extremely crude picture, but it eventually helps to rationalize the results of the various theoretical models and simulations. 

Here, we note only that the properties computed from these models are extremely sensitive to how the molecular cavity (solute/continuum interface) is constructed, and that nonelectrostatic solvation effects are typically (though not always ) neglected in the PCMs such as COSMO, GCOSMO, lEF-PCM, and SS(V)PE that are derived from Poisson s equation for continuum electrostatics. In contrast, such effects are built into the empirical SMx models and are crucial to accurate prediction of solvation free energies. " It is unclear how the neglect of nonelectrostatic effects might impact the calculation of anion VDEs cavitation effect should cancel, but dispersion effects may not, as the anion is intrinsically more polarizable. One may hope that these effects will disappear if a sufficiently large number of explicit solvent molecules is included as part of the QM solute. 

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